MA209-5-SP: Introduction to Numerical Methods
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to year(s) of study:
Available to Study Abroad / Exchange Students: Yes Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No Co-requisites: MA206-5-AU
|Module is taught during the following terms
The module gives an introduction to practical techniques for carrying out numerical computations on a range of mathematical problems. Students will be expected to have an elementary acquaintance with Matlab. (An introductory session on Matlab will be provided for those who need it.)
1. An Introduction to Practical Computation
- Simple examples
2. Solving single nonlinear equations
- Bisection Method
- Regula Falsi
- Newton's Method
3. Numerical linear algebra
- Gaussian Elimination
- Partial pivoting
- Iterative methods
4. Numerical solution of ordinary differential equations
- Euler's Method
- Runge-Kutta Methods
- Linear Multi-step Methods
5. Simple approximation
- Polynomial interpolation
- Optimal interpolation points
- Fourier and Trigonometric Series
On completion of the module students should be able to:
- appreciate the processes and pitfalls of mathematical approximation
- demonstrate knowledge and understanding of mathematical computing
- motivate and describe the derivation of the numerical algorithms covered in the module
- carry out simple numerical processes "by hand"
- implement and execute algorithms in Matlab
- evaluate, contrast and reflect upon the numerical results arising from different algorithms.
Learning and Teaching Methods
This module runs at 3 hours per week in the Spring term. There are two lectures and one class / laboratory each week. In the Summer term 3 revision lectures are given.
30 per cent Coursework Mark, 70 per cent Exam Mark
The coursework will involve five practical assignments, one associated with each of the five major headings in the module description above.
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information
Exam Duration and Period
2:00 hour exam during Summer Examination period.
- Recommended Reading:
C. Moler, Numerical Computing with Matlab. SIAM (2004)
B. Bradie, A Friendly Introduction to Numerical Analysis. Prentice-Hall (2005).
J. Mathews and K. Fink, Numerical Methods using Matlab, (4th ed.) Prentice-Hall (2004)